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Question 19

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Let FF and GG be continuous differentiable functions with F(x)=h(x)G(x)F'(x)=h(x)G(x) and G(x)=h(x)F(x)G'(x)=h(x)F(x). If F(0)=1F(0)=1, F(1)=257F(1)=\frac{25}7, G(0)=0G(0)=0, and G(1)=247G(1)=\frac{24}7, find 01h(x)dx\int_0^1h(x)\,dx.

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